An Intriguing One

Its mathematician's intuition, you look at a problem and it gives a resonance of an 'intriguing,deep impact' result. One such thing, I came across recently.

Problem: For any two positive real numbers 'a' and 'b' such that a>=b.Find the maximum number of points that can be included within the circle of radius 'a' which are separated by at least a distance 'b'.

generalized problem said, max number of points within a enclosed 'k' dimensional surface where distance between the points is greater than or equal to a given positive real number.

P.S : I am clueless.